Problem: The sum of $6$ consecutive integers is $51$. What is the fourth number in this sequence?
Solution: Call the first number in the sequence $x$ The next integer in the sequence is $x + 1$ The sum of the $6$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 51$ $6x + 15= 51$ $6x = 36$ $x = 6$ Since $x$ is the first number, $x + 3$ is the fourth integer. Thus, the fourth number in the sequence is $9$.